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We consider the James and Schäffer type constants recently introduced by Takahashi. We prove an equality between James (resp. Schäffer) type constants and the modulus of convexity (resp. smoothness). By using these equalities, we obtain some estimates for the new constants in terms of the James constant. As a result, we improve an inequality between the Zbăganu and James constants.
Fenghui Wang, and Changsen Yang. "An inequality between the James and James type constants in Banach spaces." Studia Mathematica 201.2 (2010): 191-201. <http://eudml.org/doc/285837>.
@article{FenghuiWang2010, abstract = {We consider the James and Schäffer type constants recently introduced by Takahashi. We prove an equality between James (resp. Schäffer) type constants and the modulus of convexity (resp. smoothness). By using these equalities, we obtain some estimates for the new constants in terms of the James constant. As a result, we improve an inequality between the Zbăganu and James constants.}, author = {Fenghui Wang, Changsen Yang}, journal = {Studia Mathematica}, keywords = {James constants; modulus of convexity; Schäffer constants}, language = {eng}, number = {2}, pages = {191-201}, title = {An inequality between the James and James type constants in Banach spaces}, url = {http://eudml.org/doc/285837}, volume = {201}, year = {2010}, }
TY - JOUR AU - Fenghui Wang AU - Changsen Yang TI - An inequality between the James and James type constants in Banach spaces JO - Studia Mathematica PY - 2010 VL - 201 IS - 2 SP - 191 EP - 201 AB - We consider the James and Schäffer type constants recently introduced by Takahashi. We prove an equality between James (resp. Schäffer) type constants and the modulus of convexity (resp. smoothness). By using these equalities, we obtain some estimates for the new constants in terms of the James constant. As a result, we improve an inequality between the Zbăganu and James constants. LA - eng KW - James constants; modulus of convexity; Schäffer constants UR - http://eudml.org/doc/285837 ER -